SOCHI, Russia — A new format was supposed to make the Olympic women’s hockey tournament more competitive after Vancouver, when then-IOC president Jacques Rogge hinted that the sport could be kicked out of the Winter Games.

One day into the Sochi Games and the winners look the same.

The United States and Canada won their openers at the Shayba Arena on Saturday despite changes that were supposed to bring some of the marquee matchups into the round-robin. The Americans beat Finland 3-1 and Canada beat Switzerland 5-0, showing that the North American dominance of the sport is still supreme.

“It’s the best result we’ve ever had against Canada,” Swiss goalie Florence Schelling said after making 64 saves in a 5-0 loss to the three-time defending champions. “It shows we have improved.”

A spate of blowouts in 2010 led hockey’s international governing body to place the four top teams in their own group, with the next four in a group of their own. The teams in Group A will compete for two spots in the semifinals and two in the quarterfinals; two other spots in the quarterfinals will go to the top two teams in Group B.

That means the United States faced Finland, the 2010 bronze medalist, in the Sochi opener instead of China, which it beat 12-1 to start the Vancouver Games. Finnish goalie Noora Raty, a two-time NCAA champion, gave up Hilary Knight’s goal 53 seconds into the game but stopped 40 shots to keep it close from there.

“I always know that when you face the U.S. or Canada, it’s going to be 40 or 50 shots,” she said. “They are the huge favorites and we are the underdog.”

Knight is one of two members of the U.S. team who attended Choate Rosemary Hall in Wallingford, Conn. Choate alum Phoebe Staenze plays for Switzerland.

Jesse Vetter stopped 14 shots for the Americans. Kelli Stack and Alex Carpenter also scored for the Americans, each getting a fortunate bounce on what Finnish coach Mika Pieniniemi called “an ‘oops’ goal.”

The U.S. players had said they would need ugly goals to beat Raty, who stopped 58 American shots in November in an upset victory in Lake Placid, N.Y., and coach Katey Stone made no apologies for how the puck went in.

“We talk a lot about how there are no snapshots on the scorecard,” Stone said. “If it’s an ugly one, it’s an ugly one. And sometimes against a fantastic goaltender that’s how you have to get it done.”

All-time Olympic leading scorer Hayley Wickenheiser added to her record with her 17th career Winter Games goal to lead Canada in the late game. Wickenheiser has participated in every Olympics since women’s hockey was made an official sport in 1998, and she has scored in every one.

Rebecca Johnston had a goal and two assists and Marie-Philip Poulin had one of each for Canada, which hadn’t ever beaten the Swiss by fewer than six goals in any competition. Charline Labonte stopped all 14 shots she faced for the shutout.

The U.S. plays Switzerland on Monday, and Canada plays Finland. The North Americans will meet in the round-robin on Feb. 12 — one of the benefits of the new format — and they’re still on track to play in the gold medal game on Feb. 20.